Tow harness to tow socket help

So my Tacoma didn't come with a towing package and I'm planning on wiring up the harness. At the end of the harness is a 4 pin connection. Is there any way (enough room) to connect to the 7 pin on the back of the socket without splicing wires? Or an outlet with a 4 pin connection on the socket. These are the items I'm planning on purchasing.
https://www.tekonsha.com/product/118685_tow-harness-t-connector-assembly
https://hopkinstowingsolutions.com/?t=products/vehicle-wiring-kits/vehicle-specific/40974

 

My 2.7 came with an installed OEM hitch and 4 pin wiring. I ordered a 7 pin kit from etrailer and it allowed me to plug my existing 4 pin into it and I then ran wires for 12v power to trailer and the brake controller.
I put a relay in the 12v line to be certain I didn’t drain my vehicle battery when the truck was off and trailer plug still connected.

 

This is the One I used.
https://www.etrailer.com/Accessories-and-Parts/etrailer/ETBC7.html